## The Annals of Applied Probability

### Social contact processes and the partner model

#### Abstract

We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_{0}$ with the property that if $R_{0}<1$ the infection dies out by time $O(\log N)$, while if $R_{0}>1$ the infection survives for an amount of time $e^{\gamma N}$ for some $\gamma>0$ and hovers around a uniquely determined metastable proportion of infectious individuals. The proof in both cases relies on comparison to a set of mean-field equations when the infection is widespread, and to a branching process when the infection is sparse.

#### Article information

Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1297-1328.

Dates
Revised: April 2015
First available in Project Euclid: 14 June 2016

https://projecteuclid.org/euclid.aoap/1465905004

Digital Object Identifier
doi:10.1214/15-AAP1117

Mathematical Reviews number (MathSciNet)
MR3513591

Zentralblatt MATH identifier
1345.60115

#### Citation

Foxall, Eric; Edwards, Roderick; van den Driessche, P. Social contact processes and the partner model. Ann. Appl. Probab. 26 (2016), no. 3, 1297--1328. doi:10.1214/15-AAP1117. https://projecteuclid.org/euclid.aoap/1465905004

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